Simple fit¶
In this example we consider the inversion problem of the mid-transit times for a three-planet system. We show the standard way for using nauyaca in order to estimate the planet masses and orbits. This is a synthetic planetary system whose transit ephemeris have been calculated as described in Canul et al. (2021). Unlike the two-planet system considered in the Documentation, here we exemplify the usage of the minimum code necessary to invert the problem. We obtain finally the MCMC posteriors and make a pair of figures to evaluate our results.
In [1]:
import nauyaca as nau
import matplotlib.pyplot as plt
import numpy as np
The input data is in the directory
In [2]:
directory = "./inputs/"
Defining planet objects: Names, boundaries and TTVs data
In [3]:
# Planet 1
P1 = nau.SetPlanet('Planet-b')
P1.mass = [0.001, 10] # Explore super-Earth mass range
P1.period = [10.47, 10.48]
P1.ecc = [0.0, 0.1]
P1.inclination = [90,90] # Constant!
P1.ascending_node = [60, 120]
P1.load_ttvs(directory + "3pl_planet1_ttvs.dat")
In [4]:
# Planet 2
P2 = nau.SetPlanet('Planet-c')
P2.mass = [0.001, 10]
P2.period = [14.10, 14.11]
P2.ecc = [0.0, 0.1]
P2.inclination = [85,95]
P2.ascending_node = [60, 120]
P2.load_ttvs(directory + "3pl_planet2_ttvs.dat")
In [5]:
# Planet 3
P3 = nau.SetPlanet('Planet-d')
P3.mass = [0.001, 10]
P3.period = [23.57, 23.58]
P3.ecc = [0.0, 0.1]
P3.inclination = [90.3,90.3] # Constant!
P3.ascending_node = [88.5, 88.5] # Constant!
P3.load_ttvs(directory + "3pl_planet3_ttvs.dat")
Creating the Planetary System object
In [6]:
PS = nau.PlanetarySystem("MySystem", mstar=0.522, rstar=0.4422)
PS.add_planets([P1, P2, P3])
# Print a summary of the Planetary System
print(PS)
--> Parameter -mass- of planet -Planet-b- set to lower physical limit: 0.0123032
--> Parameter -ecc- of planet -Planet-b- set to lower physical limit: 1e-06
--> Parameter -mass- of planet -Planet-c- set to lower physical limit: 0.0123032
--> Parameter -ecc- of planet -Planet-c- set to lower physical limit: 1e-06
--> Parameter -mass- of planet -Planet-d- set to lower physical limit: 0.0123032
--> Parameter -ecc- of planet -Planet-d- set to lower physical limit: 1e-06
=========== Planetary System Summary ===========
--> Parameter -mass- of planet -Planet-b- set to lower physical limit: 0.0123032
--> Parameter -ecc- of planet -Planet-b- set to lower physical limit: 1e-06
--> Parameter -mass- of planet -Planet-c- set to lower physical limit: 0.0123032
--> Parameter -ecc- of planet -Planet-c- set to lower physical limit: 1e-06
--> Parameter -mass- of planet -Planet-d- set to lower physical limit: 0.0123032
--> Parameter -ecc- of planet -Planet-d- set to lower physical limit: 1e-06
System: MySystem
Mstar: 0.522 Msun | Rstar: 0.4422 Rsun
Number of planets: 3
Planet information:
------
Planet1: Planet-b
Boundaries:
mass: (0.0123032, 10) [M_earth]
period: (10.47, 10.48) [d]
ecc: (1e-06, 0.1)
inclination: (90, 90) [deg]
argument: (0.0, 360) [deg]
mean_anomaly: (0.0, 360) [deg]
ascending_node: (60, 120) [deg]
TTVs: True
------
Planet2: Planet-c
Boundaries:
mass: (0.0123032, 10) [M_earth]
period: (14.1, 14.11) [d]
ecc: (1e-06, 0.1)
inclination: (85, 95) [deg]
argument: (0.0, 360) [deg]
mean_anomaly: (0.0, 360) [deg]
ascending_node: (60, 120) [deg]
TTVs: True
------
Planet3: Planet-d
Boundaries:
mass: (0.0123032, 10) [M_earth]
period: (23.57, 23.58) [d]
ecc: (1e-06, 0.1)
inclination: (90.3, 90.3) [deg]
argument: (0.0, 360) [deg]
mean_anomaly: (0.0, 360) [deg]
ascending_node: (88.5, 88.5) [deg]
TTVs: True
Simulation attributes:
Reference epoch of the solutions (t0): 0.0 [JD]
Total time of TTVs data (ftime): 1359.0 [days]
Timestep of the simulations (dt): 0.34874 [days]
From the output above it is seen that the observations span around ~1360 days. Setting the simulation attribute ftime = 500 will discard all the observations greater than 500 days. It is useful when you want to quickly explore the possible solutions without evaluating all the transits, as in the case of this example. If not changed, these are the default simulations attributes calculated by nauyaca. Let's change the final time to exemplify the usage:
In [7]:
# Simulation attributes
# Here, t0 is the reference time of the osculating elements
PS.simulation(t0=0, ftime=500)
Save the Planetary System for further examples in json format
In [8]:
PS.save_json()
--> JSON file ./MySystem.json saved
Running the optimizers.¶
Let's run the optimizers to build an informed initial guess for the MCMC. Increase the number of solutions and specify an adequate number of cores to run in parallel.
In [9]:
optim = nau.Optimizers(PS, nsols=120, cores=8)
opt_solutions = optim.run()
=========== OPTIMIZATION ===========
--> Starting date: 2021-08-16 15:17
--> Finding 120 solutions using 8 cores
--> Results will be saved at:
* ./MySystem_cube.opt (normalized)
* ./MySystem_phys.opt (physical)
--> Reference time of the solutions: 0 [days]
- - - - - - - - - - - - - - - - - - - - -
Solution | chi square from optimizers
- - - - - - - - - - - - - - - - - - - - -
3 | 346729722.432 --> 624449.039 --> 373721.785
7 | 304026464.383 --> 183995389.906 --> 140560.172
2 | 314257803.181 --> 1002867.079 --> 108913.637
1 | 213637841.023 --> 2065509.063 --> 158532.608
4 | 418220204.410 --> 22166.197 --> 8928.114
5 | 298811335.711 --> 2716081.077 --> 316567.898
6 | 431389099.830 --> 122309874.901 --> 87801613.464
8 | 889653777.894 --> 1281292.026 --> 19199.064
13 | 158273363.622 --> 490365.607 --> 78315.261
9 | 456897724.394 --> 370280.636 --> 140265.742
14 | 397656483.107 --> 922399.208 --> 591199.157
10 | 260566694.323 --> 181151.896 --> 4881.841
16 | 234796812.653 --> 449850.549 --> 67313.017
11 | 148898864.303 --> 353175.804 --> 53973.620
12 | 178962139.599 --> 60867595.837 --> 7628284.745
17 | 516034845.454 --> 423387.940 --> 13343.936
15 | 384999688.191 --> 191988447.004 --> 521612.242
18 | 405711108.241 --> 560983.627 --> 200128.925
20 | 210344260.452 --> 117510.509 --> 7852.728
19 | 388309290.339 --> 68024582.995 --> 24213175.834
22 | 145549898.313 --> 281954.405 --> 4957.888
23 | 133378273.952 --> 5570913.565 --> 85726.864
21 | 625504212.585 --> 99422.347 --> 3157.475
24 | 253345625.268 --> 80978.065 --> 7336.384
25 | 264638882.065 --> 213718.551 --> 51542.953
27 | 310660032.164 --> 8518696.793 --> 908621.180
26 | 212232818.647 --> 2342336.070 --> 43712.626
28 | 430677946.380 --> 257562316.284 --> 185894784.777
30 | 132493737.877 --> 1507966.295 --> 117161.748
29 | 423289719.783 --> 247859.784 --> 1454.820
31 | 51301611.840 --> 69367.194 --> 23610.405
32 | 174424046.399 --> 5120435.247 --> 75686.150
33 | 376163374.533 --> 582827.612 --> 358622.329
34 | 49612272.719 --> 6740820.381 --> 1070811.225
38 | 319138346.520 --> 19011.271 --> 10373.189
35 | 409230903.125 --> 525551.875 --> 102216.894
36 | 164175477.837 --> 508460.901 --> 80489.879
41 | 358094199.337 --> 72559.967 --> 15272.441
37 | 142429009.152 --> 375570.561 --> 104733.362
39 | 399791173.006 --> 155108.583 --> 5027.105
40 | 100796286.417 --> 2911186.877 --> 675776.472
46 | 418789928.463 --> 183499.843 --> 18596.245
48 | 319609136.627 --> 1715402.644 --> 56863.031
42 | 369590229.425 --> 440506.709 --> 3253.099
43 | 233630283.999 --> 2307141.476 --> 301502.659
44 | 294956040.182 --> 127079554.442 --> 95401.156
45 | 40561133.408 --> 36613.172 --> 2405.455
47 | 67925493.191 --> 2346714.729 --> 108508.380
49 | 157546353.572 --> 312182.123 --> 67156.338
50 | 128561872.357 --> 5105844.548 --> 69987.416
54 | 272762489.642 --> 604729.256 --> 25282.381
51 | 254124213.557 --> 20151047.536 --> 582304.418
52 | 145313542.853 --> 552853.759 --> 182956.616
53 | 135658760.401 --> 562505.720 --> 105211.244
55 | 36412612.711 --> 347275.326 --> 50459.186
56 | 282195145.259 --> 254379.809 --> 12144.910
59 | 544614069.610 --> 208200.495 --> 88561.843
61 | 192957905.032 --> 21979.837 --> 11208.754
58 | 416424985.632 --> 4461296.035 --> 219345.314
57 | 73201284.348 --> 43578301.596 --> 142320.186
60 | 62045939.292 --> 1696315.798 --> 773737.829
62 | 7168972.411 --> 330621.745 --> 76713.875
65 | 307089870.236 --> 171350.202 --> 29220.137
63 | 269851010.936 --> 293902.986 --> 266217.100
64 | 267879608.926 --> 2589212.467 --> 81883.846
66 | 198313652.509 --> 175293116.665 --> 155043.910
67 | 122695680.215 --> 2757443.638 --> 962184.320
68 | 152844160.324 --> 549399.554 --> 62485.247
69 | 62829474.896 --> 894912.168 --> 46893.634
72 | 160432381.377 --> 1508781.854 --> 68537.568
70 | 113852241.340 --> 616797.568 --> 119360.707
73 | 20427813.492 --> 530709.584 --> 88377.694
71 | 560391463.861 --> 35345994.529 --> 12815331.180
76 | 283100345.641 --> 120086.126 --> 90218.208
74 | 181937549.311 --> 491891.913 --> 28973.372
82 | 53974919.888 --> 47442.576 --> 47282.749
77 | 80105199.026 --> 173270.607 --> 40507.094
75 | 130253754.869 --> 203114.545 --> 2151.125
78 | 59572472.502 --> 16179326.134 --> 1880427.704
79 | 99234271.941 --> 532891.025 --> 176015.448
80 | 198980902.053 --> 299144.279 --> 81486.700
81 | 107065124.231 --> 6390269.934 --> 222344.654
83 | 75473980.461 --> 18178.058 --> 2514.744
90 | 552607499.838 --> 93959.754 --> 68585.054
87 | 315412348.985 --> 544789.418 --> 246167.931
84 | 193359725.025 --> 1185337.135 --> 41309.819
85 | 53386792.595 --> 3482934.027 --> 539779.493
86 | 341122660.194 --> 667316.714 --> 12248.771
89 | 98072196.762 --> 4275855.283 --> 87089.925
88 | 159258577.910 --> 28689.898 --> 4976.262
91 | 179217844.361 --> 49724707.160 --> 1876083.350
94 | 136190941.886 --> 777430.880 --> 273704.629
97 | 438793708.926 --> 51055.013 --> 4432.207
96 | 182073531.224 --> 155909.551 --> 93717.919
92 | 187884513.974 --> 398947.979 --> 35052.885
93 | 503100850.004 --> 422803921.033 --> 27933.518
95 | 186029729.835 --> 36750543.648 --> 2473857.297
98 | 144195383.734 --> 64201317.984 --> 176385.834
99 | 110306473.627 --> 479727.107 --> 117672.458
100 | 478080117.732 --> 200936.494 --> 98159.303
102 | 256038662.586 --> 15280476.048 --> 3432422.680
101 | 220416863.741 --> 94149194.779 --> 20314.593
104 | 665754887.868 --> 614208799.014 --> 419808049.779
103 | 103558452.145 --> 279909.404 --> 26620.828
105 | 261989312.601 --> 139058910.059 --> 25268835.291
106 | 319150632.131 --> 134455981.300 --> 277784.896
107 | 399893342.736 --> 91480.759 --> 4162.153
108 | 327510069.752 --> 3634026.101 --> 2005594.977
109 | 224287112.446 --> 27139.582 --> 3155.901
110 | 165413403.460 --> 284563.314 --> 12423.351
112 | 121235052.016 --> 61122445.535 --> 914715.052
113 | 10876738.520 --> 128536.809 --> 6833.191
111 | 309958627.607 --> 174546936.867 --> 161239.546
114 | 674530468.420 --> 227966.216 --> 39389.739
115 | 284835491.612 --> 187313.339 --> 119934.728
117 | 150141417.517 --> 27853511.019 --> 11585339.846
116 | 472599524.026 --> 344860605.281 --> 277806176.029
118 | 320020213.088 --> 133550153.043 --> 593210.438
120 | 116518781.432 --> 775986.710 --> 187118.665
119 | 170123789.070 --> 66663194.923 --> 415345.761
Elapsed time in optimization: 17.689 minutes
Running the MCMC.¶
Here, we set the kwarg 'opt_data' with the optimizer results, but many other kwargs must be given in order to internally create initial walkers.
Try increasing the number of iterations, walkers or temperatures
In [11]:
mcmc = nau.MCMC(PS,
tmax=100, # Maximum temperature in ladder (see ptemcee documentation)
itmax=12000, # Maximum number of iterations
intra_steps=100, # thinning factor
cores=8, # Cores to run in parallel
opt_data=np.genfromtxt('MySystem_cube.opt') , # Solutions from optimizers (cube).
# It can also be the variable -opt_solutions-
distribution='Ladder', # A strategy to initialize walkers
fbest=0.05, # A fraction of the best optimizer results
nwalkers=60, # Number of walkers
ntemps=12 # Number of temperatures
)
mcmc.run()
--> Selected distribution: Ladder
6 of 120 solutions taken
=========== PARALLEL-TEMPERING MCMC ===========
--> Starting date: 2021-08-16 20:21
--> Reference epoch of the solutions: 0 [JD]
--> Results will be saved at: ./MySystem.hdf5
--> MCMC parameters:
-ntemps: 12
-nwalkers: 60
-itmax: 12000
-intra_steps: 100
--------- Iteration: 100
Mean tau Temp 0: 0.828
Accepted swap fraction in Temp 0: 0.049
Mean acceptance fraction Temp 0: 0.243
Mean log-likelihood: -424.284
Mean log-posterior: -424.284
Current log-posterior dispersion: 560.487
Current MAP: (0, 3) -211.424
Saving time: 0.01350 sec
Elapsed time: 0.4259 min
--------- Iteration: 200
Mean tau Temp 0: 1.617
Accepted swap fraction in Temp 0: 0.026
Mean acceptance fraction Temp 0: 0.32
Mean log-likelihood: -90.842
Mean log-posterior: -90.842
Current log-posterior dispersion: 98.647
Current MAP: (0, 5) -51.791
Saving time: 0.01714 sec
Elapsed time: 0.9258 min
--------- Iteration: 300
Mean tau Temp 0: 2.391
Accepted swap fraction in Temp 0: 0.017
Mean acceptance fraction Temp 0: 0.336
Mean log-likelihood: 35.286
Mean log-posterior: 35.286
Current log-posterior dispersion: 13.419
Current MAP: (0, 51) 68.62
Saving time: 0.01820 sec
Elapsed time: 1.3836 min
--------- Iteration: 400
Mean tau Temp 0: 3.166
Accepted swap fraction in Temp 0: 0.013
Mean acceptance fraction Temp 0: 0.345
Mean log-likelihood: 134.9
Mean log-posterior: 134.9
Current log-posterior dispersion: 11.051
Current MAP: (0, 57) 152.555
Saving time: 0.01827 sec
Elapsed time: 1.8368 min
--------- Iteration: 500
Mean tau Temp 0: 3.927
Accepted swap fraction in Temp 0: 0.01
Mean acceptance fraction Temp 0: 0.344
Mean log-likelihood: 185.45
Mean log-posterior: 185.45
Current log-posterior dispersion: 6.561
Current MAP: (0, 51) 201.731
Saving time: 0.02690 sec
Elapsed time: 2.3197 min
--------- Iteration: 600
Mean tau Temp 0: 4.683
Accepted swap fraction in Temp 0: 0.009
Mean acceptance fraction Temp 0: 0.343
Mean log-likelihood: 224.662
Mean log-posterior: 224.662
Current log-posterior dispersion: 6.293
Current MAP: (0, 26) 237.642
Saving time: 0.02732 sec
Elapsed time: 2.9396 min
--------- Iteration: 700
Mean tau Temp 0: 5.448
Accepted swap fraction in Temp 0: 0.007
Mean acceptance fraction Temp 0: 0.339
Mean log-likelihood: 266.886
Mean log-posterior: 266.886
Current log-posterior dispersion: 7.871
Current MAP: (0, 53) 291.227
Saving time: 0.02768 sec
Elapsed time: 3.5024 min
--------- Iteration: 800
Mean tau Temp 0: 6.207
Accepted swap fraction in Temp 0: 0.006
Mean acceptance fraction Temp 0: 0.333
Mean log-likelihood: 302.02
Mean log-posterior: 302.02
Current log-posterior dispersion: 9.935
Current MAP: (0, 3) 322.285
Saving time: 0.02479 sec
Elapsed time: 4.0547 min
--------- Iteration: 900
Mean tau Temp 0: 6.946
Accepted swap fraction in Temp 0: 0.006
Mean acceptance fraction Temp 0: 0.329
Mean log-likelihood: 363.12
Mean log-posterior: 363.12
Current log-posterior dispersion: 14.69
Current MAP: (0, 41) 386.731
Saving time: 0.02411 sec
Elapsed time: 4.5376 min
--------- Iteration: 1000
Mean tau Temp 0: 7.623
Accepted swap fraction in Temp 0: 0.005
Mean acceptance fraction Temp 0: 0.331
Mean log-likelihood: 422.722
Mean log-posterior: 422.722
Current log-posterior dispersion: 6.12
Current MAP: (0, 41) 435.916
Saving time: 0.02302 sec
Elapsed time: 4.9947 min
--------- Iteration: 1100
Mean tau Temp 0: 8.295
Accepted swap fraction in Temp 0: 0.005
Mean acceptance fraction Temp 0: 0.33
Mean log-likelihood: 451.269
Mean log-posterior: 451.269
Current log-posterior dispersion: 6.722
Current MAP: (0, 55) 465.666
Saving time: 0.02319 sec
Elapsed time: 5.4427 min
--------- Iteration: 1200
Mean tau Temp 0: 8.98
Accepted swap fraction in Temp 0: 0.004
Mean acceptance fraction Temp 0: 0.328
Mean log-likelihood: 469.186
Mean log-posterior: 469.186
Current log-posterior dispersion: 4.712
Current MAP: (0, 14) 479.871
Saving time: 0.02420 sec
Elapsed time: 5.8919 min
--------- Iteration: 1300
Mean tau Temp 0: 9.669
Accepted swap fraction in Temp 0: 0.004
Mean acceptance fraction Temp 0: 0.324
Mean log-likelihood: 486.506
Mean log-posterior: 486.506
Current log-posterior dispersion: 5.892
Current MAP: (0, 14) 497.526
Saving time: 0.02395 sec
Elapsed time: 6.3419 min
--------- Iteration: 1400
Mean tau Temp 0: 10.355
Accepted swap fraction in Temp 0: 0.004
Mean acceptance fraction Temp 0: 0.318
Mean log-likelihood: 497.402
Mean log-posterior: 497.402
Current log-posterior dispersion: 7.268
Current MAP: (0, 41) 511.691
Saving time: 0.02399 sec
Elapsed time: 6.7907 min
--------- Iteration: 1500
Mean tau Temp 0: 11.041
Accepted swap fraction in Temp 0: 0.003
Mean acceptance fraction Temp 0: 0.311
Mean log-likelihood: 510.543
Mean log-posterior: 510.543
Current log-posterior dispersion: 9.358
Current MAP: (0, 20) 524.461
Saving time: 0.02479 sec
Elapsed time: 7.2338 min
--------- Iteration: 1600
Mean tau Temp 0: 11.728
Accepted swap fraction in Temp 0: 0.003
Mean acceptance fraction Temp 0: 0.305
Mean log-likelihood: 522.979
Mean log-posterior: 522.979
Current log-posterior dispersion: 11.81
Current MAP: (0, 36) 537.934
Saving time: 0.02636 sec
Elapsed time: 7.6832 min
--------- Iteration: 1700
Mean tau Temp 0: 12.411
Accepted swap fraction in Temp 0: 0.003
Mean acceptance fraction Temp 0: 0.297
Mean log-likelihood: 532.267
Mean log-posterior: 532.267
Current log-posterior dispersion: 12.53
Current MAP: (0, 29) 545.766
Saving time: 0.02713 sec
Elapsed time: 8.1419 min
--------- Iteration: 1800
Mean tau Temp 0: 13.087
Accepted swap fraction in Temp 0: 0.003
Mean acceptance fraction Temp 0: 0.291
Mean log-likelihood: 538.749
Mean log-posterior: 538.749
Current log-posterior dispersion: 14.325
Current MAP: (0, 42) 555.104
Saving time: 0.02773 sec
Elapsed time: 8.5945 min
--------- Iteration: 1900
Mean tau Temp 0: 13.761
Accepted swap fraction in Temp 0: 0.003
Mean acceptance fraction Temp 0: 0.286
Mean log-likelihood: 543.365
Mean log-posterior: 543.365
Current log-posterior dispersion: 14.471
Current MAP: (0, 20) 554.683
Saving time: 0.02639 sec
Elapsed time: 9.044 min
--------- Iteration: 2000
Mean tau Temp 0: 14.431
Accepted swap fraction in Temp 0: 0.003
Mean acceptance fraction Temp 0: 0.282
Mean log-likelihood: 549.006
Mean log-posterior: 549.006
Current log-posterior dispersion: 15.968
Current MAP: (0, 10) 564.009
Saving time: 0.02797 sec
Elapsed time: 9.4877 min
--------- Iteration: 2100
Mean tau Temp 0: 15.097
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.278
Mean log-likelihood: 554.927
Mean log-posterior: 554.927
Current log-posterior dispersion: 17.048
Current MAP: (0, 20) 571.013
Saving time: 0.02898 sec
Elapsed time: 9.9496 min
--------- Iteration: 2200
Mean tau Temp 0: 15.756
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.274
Mean log-likelihood: 559.502
Mean log-posterior: 559.502
Current log-posterior dispersion: 18.202
Current MAP: (0, 37) 573.246
Saving time: 0.02953 sec
Elapsed time: 10.4069 min
--------- Iteration: 2300
Mean tau Temp 0: 16.411
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.27
Mean log-likelihood: 562.637
Mean log-posterior: 562.637
Current log-posterior dispersion: 19.06
Current MAP: (0, 14) 577.935
Saving time: 0.02993 sec
Elapsed time: 10.8561 min
--------- Iteration: 2400
Mean tau Temp 0: 17.06
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.266
Mean log-likelihood: 565.007
Mean log-posterior: 565.007
Current log-posterior dispersion: 19.526
Current MAP: (0, 14) 578.988
Saving time: 0.03072 sec
Elapsed time: 11.3083 min
--------- Iteration: 2500
Mean tau Temp 0: 17.705
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.263
Mean log-likelihood: 568.0
Mean log-posterior: 568.0
Current log-posterior dispersion: 20.207
Current MAP: (0, 33) 582.951
Saving time: 0.03117 sec
Elapsed time: 11.7576 min
--------- Iteration: 2600
Mean tau Temp 0: 18.346
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.26
Mean log-likelihood: 571.2
Mean log-posterior: 571.2
Current log-posterior dispersion: 20.868
Current MAP: (0, 20) 583.114
Saving time: 0.03046 sec
Elapsed time: 12.2115 min
--------- Iteration: 2700
Mean tau Temp 0: 18.982
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.256
Mean log-likelihood: 572.138
Mean log-posterior: 572.138
Current log-posterior dispersion: 21.277
Current MAP: (0, 27) 586.148
Saving time: 0.03131 sec
Elapsed time: 12.6624 min
--------- Iteration: 2800
Mean tau Temp 0: 19.613
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.253
Mean log-likelihood: 574.228
Mean log-posterior: 574.228
Current log-posterior dispersion: 21.897
Current MAP: (0, 40) 590.158
Saving time: 0.03253 sec
Elapsed time: 13.1092 min
--------- Iteration: 2900
Mean tau Temp 0: 20.24
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.249
Mean log-likelihood: 575.57
Mean log-posterior: 575.57
Current log-posterior dispersion: 22.242
Current MAP: (0, 25) 591.442
Saving time: 0.03333 sec
Elapsed time: 13.5571 min
--------- Iteration: 3000
Mean tau Temp 0: 20.859
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.246
Mean log-likelihood: 577.25
Mean log-posterior: 577.25
Current log-posterior dispersion: 23.039
Current MAP: (0, 25) 591.687
Saving time: 0.03467 sec
Elapsed time: 14.0036 min
--------- Iteration: 3100
Mean tau Temp 0: 21.471
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.243
Mean log-likelihood: 578.525
Mean log-posterior: 578.525
Current log-posterior dispersion: 23.132
Current MAP: (0, 25) 591.864
Saving time: 0.01478 sec
Elapsed time: 14.4511 min
--------- Iteration: 3200
Mean tau Temp 0: 22.077
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.239
Mean log-likelihood: 579.153
Mean log-posterior: 579.153
Current log-posterior dispersion: 22.764
Current MAP: (0, 2) 593.515
Saving time: 0.02080 sec
Elapsed time: 14.8983 min
--------- Iteration: 3300
Mean tau Temp 0: 22.674
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.236
Mean log-likelihood: 580.124
Mean log-posterior: 580.124
Current log-posterior dispersion: 22.585
Current MAP: (0, 29) 594.479
Saving time: 0.02127 sec
Elapsed time: 15.3648 min
--------- Iteration: 3400
Mean tau Temp 0: 23.262
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.233
Mean log-likelihood: 580.355
Mean log-posterior: 580.355
Current log-posterior dispersion: 22.734
Current MAP: (0, 5) 596.644
Saving time: 0.02195 sec
Elapsed time: 15.8088 min
--------- Iteration: 3500
Mean tau Temp 0: 23.844
Accepted swap fraction in Temp 0: 0.001
Mean acceptance fraction Temp 0: 0.23
Mean log-likelihood: 581.618
Mean log-posterior: 581.618
Current log-posterior dispersion: 23.279
Current MAP: (0, 46) 596.941
Saving time: 0.02218 sec
Elapsed time: 16.2564 min
--------- Iteration: 3600
Mean tau Temp 0: 24.416
Accepted swap fraction in Temp 0: 0.001
Mean acceptance fraction Temp 0: 0.228
Mean log-likelihood: 581.77
Mean log-posterior: 581.77
Current log-posterior dispersion: 24.7
Current MAP: (0, 39) 595.179
Saving time: 0.02183 sec
Elapsed time: 16.7083 min
--------- Iteration: 3700
Mean tau Temp 0: 24.978
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.225
Mean log-likelihood: 582.799
Mean log-posterior: 582.799
Current log-posterior dispersion: 22.96
Current MAP: (0, 2) 596.996
Saving time: 0.02174 sec
Elapsed time: 17.1579 min
--------- Iteration: 3800
Mean tau Temp 0: 25.531
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.222
Mean log-likelihood: 583.644
Mean log-posterior: 583.644
Current log-posterior dispersion: 22.174
Current MAP: (0, 18) 598.441
Saving time: 0.02233 sec
Elapsed time: 17.6063 min
--------- Iteration: 3900
Mean tau Temp 0: 26.072
Accepted swap fraction in Temp 0: 0.002
Mean acceptance fraction Temp 0: 0.219
Mean log-likelihood: 584.212
Mean log-posterior: 584.212
Current log-posterior dispersion: 21.585
Current MAP: (0, 18) 596.615
Saving time: 0.02369 sec
Elapsed time: 18.0493 min
--------- Iteration: 4000
Mean tau Temp 0: 26.602
Accepted swap fraction in Temp 0: 0.003
Mean acceptance fraction Temp 0: 0.217
Mean log-likelihood: 584.141
Mean log-posterior: 584.141
Current log-posterior dispersion: 21.994
Current MAP: (0, 48) 598.283
Saving time: 0.02302 sec
Elapsed time: 18.5025 min
--------- Iteration: 4100
Mean tau Temp 0: 27.123
Accepted swap fraction in Temp 0: 0.003
Mean acceptance fraction Temp 0: 0.214
Mean log-likelihood: 584.948
Mean log-posterior: 584.948
Current log-posterior dispersion: 20.052
Current MAP: (0, 22) 600.261
Saving time: 0.02417 sec
Elapsed time: 18.9665 min
--------- Iteration: 4200
Mean tau Temp 0: 27.634
Accepted swap fraction in Temp 0: 0.004
Mean acceptance fraction Temp 0: 0.212
Mean log-likelihood: 585.856
Mean log-posterior: 585.856
Current log-posterior dispersion: 18.315
Current MAP: (0, 48) 598.476
Saving time: 0.02393 sec
Elapsed time: 19.4147 min
--------- Iteration: 4300
Mean tau Temp 0: 28.131
Accepted swap fraction in Temp 0: 0.004
Mean acceptance fraction Temp 0: 0.209
Mean log-likelihood: 586.419
Mean log-posterior: 586.419
Current log-posterior dispersion: 18.641
Current MAP: (0, 49) 599.397
Saving time: 0.02471 sec
Elapsed time: 19.8582 min
--------- Iteration: 4400
Mean tau Temp 0: 28.619
Accepted swap fraction in Temp 0: 0.005
Mean acceptance fraction Temp 0: 0.207
Mean log-likelihood: 587.017
Mean log-posterior: 587.017
Current log-posterior dispersion: 18.695
Current MAP: (0, 45) 599.31
Saving time: 0.02583 sec
Elapsed time: 20.3084 min
--------- Iteration: 4500
Mean tau Temp 0: 29.094
Accepted swap fraction in Temp 0: 0.005
Mean acceptance fraction Temp 0: 0.205
Mean log-likelihood: 587.384
Mean log-posterior: 587.384
Current log-posterior dispersion: 17.007
Current MAP: (0, 45) 599.167
Saving time: 0.02672 sec
Elapsed time: 20.7644 min
--------- Iteration: 4600
Mean tau Temp 0: 29.556
Accepted swap fraction in Temp 0: 0.006
Mean acceptance fraction Temp 0: 0.202
Mean log-likelihood: 586.51
Mean log-posterior: 586.51
Current log-posterior dispersion: 18.965
Current MAP: (0, 35) 598.95
Saving time: 0.02613 sec
Elapsed time: 21.2109 min
--------- Iteration: 4700
Mean tau Temp 0: 30.005
Accepted swap fraction in Temp 0: 0.006
Mean acceptance fraction Temp 0: 0.2
Mean log-likelihood: 588.343
Mean log-posterior: 588.343
Current log-posterior dispersion: 16.142
Current MAP: (0, 45) 598.636
Saving time: 0.02592 sec
Elapsed time: 21.6597 min
--------- Iteration: 4800
Mean tau Temp 0: 30.445
Accepted swap fraction in Temp 0: 0.007
Mean acceptance fraction Temp 0: 0.198
Mean log-likelihood: 589.068
Mean log-posterior: 589.068
Current log-posterior dispersion: 15.549
Current MAP: (0, 11) 600.565
Saving time: 0.02639 sec
Elapsed time: 22.1067 min
--------- Iteration: 4900
Mean tau Temp 0: 30.867
Accepted swap fraction in Temp 0: 0.007
Mean acceptance fraction Temp 0: 0.196
Mean log-likelihood: 586.708
Mean log-posterior: 586.708
Current log-posterior dispersion: 18.199
Current MAP: (0, 15) 599.879
Saving time: 0.02792 sec
Elapsed time: 22.5474 min
--------- Iteration: 5000
Mean tau Temp 0: 31.279
Accepted swap fraction in Temp 0: 0.008
Mean acceptance fraction Temp 0: 0.194
Mean log-likelihood: 589.708
Mean log-posterior: 589.708
Current log-posterior dispersion: 14.762
Current MAP: (0, 0) 600.235
Saving time: 0.02743 sec
Elapsed time: 23.0036 min
--------- Iteration: 5100
Mean tau Temp 0: 31.627
Accepted swap fraction in Temp 0: 0.008
Mean acceptance fraction Temp 0: 0.193
Mean log-likelihood: 589.025
Mean log-posterior: 589.025
Current log-posterior dispersion: 14.048
Current MAP: (0, 11) 600.287
Saving time: 0.02769 sec
Elapsed time: 23.4508 min
--------- Iteration: 5200
Mean tau Temp 0: 31.926
Accepted swap fraction in Temp 0: 0.009
Mean acceptance fraction Temp 0: 0.191
Mean log-likelihood: 587.918
Mean log-posterior: 587.918
Current log-posterior dispersion: 16.579
Current MAP: (0, 11) 600.401
Saving time: 0.02902 sec
Elapsed time: 23.9053 min
--------- Iteration: 5300
Mean tau Temp 0: 32.182
Accepted swap fraction in Temp 0: 0.009
Mean acceptance fraction Temp 0: 0.189
Mean log-likelihood: 589.301
Mean log-posterior: 589.301
Current log-posterior dispersion: 13.706
Current MAP: (0, 8) 600.306
Saving time: 0.02986 sec
Elapsed time: 24.353 min
--------- Iteration: 5400
Mean tau Temp 0: 32.397
Accepted swap fraction in Temp 0: 0.01
Mean acceptance fraction Temp 0: 0.188
Mean log-likelihood: 588.664
Mean log-posterior: 588.664
Current log-posterior dispersion: 15.006
Current MAP: (0, 8) 600.37
Saving time: 0.03068 sec
Elapsed time: 24.8017 min
--------- Iteration: 5500
Mean tau Temp 0: 32.568
Accepted swap fraction in Temp 0: 0.01
Mean acceptance fraction Temp 0: 0.186
Mean log-likelihood: 590.335
Mean log-posterior: 590.335
Current log-posterior dispersion: 13.49
Current MAP: (0, 31) 600.642
Saving time: 0.03088 sec
Elapsed time: 25.2489 min
--------- Iteration: 5600
Mean tau Temp 0: 32.7
Accepted swap fraction in Temp 0: 0.011
Mean acceptance fraction Temp 0: 0.184
Mean log-likelihood: 589.533
Mean log-posterior: 589.533
Current log-posterior dispersion: 15.126
Current MAP: (0, 41) 600.695
Saving time: 0.03050 sec
Elapsed time: 25.6943 min
--------- Iteration: 5700
Mean tau Temp 0: 32.793
Accepted swap fraction in Temp 0: 0.011
Mean acceptance fraction Temp 0: 0.183
Mean log-likelihood: 590.742
Mean log-posterior: 590.742
Current log-posterior dispersion: 12.701
Current MAP: (0, 9) 601.694
Saving time: 0.03249 sec
Elapsed time: 26.153 min
--------- Iteration: 5800
Mean tau Temp 0: 32.851
Accepted swap fraction in Temp 0: 0.012
Mean acceptance fraction Temp 0: 0.181
Mean log-likelihood: 590.754
Mean log-posterior: 590.754
Current log-posterior dispersion: 11.793
Current MAP: (0, 38) 600.953
Saving time: 0.03457 sec
Elapsed time: 26.6203 min
--------- Iteration: 5900
Mean tau Temp 0: 32.873
Accepted swap fraction in Temp 0: 0.012
Mean acceptance fraction Temp 0: 0.18
Mean log-likelihood: 589.846
Mean log-posterior: 589.846
Current log-posterior dispersion: 13.097
Current MAP: (0, 54) 601.259
Saving time: 0.03307 sec
Elapsed time: 27.0758 min
--------- Iteration: 6000
Mean tau Temp 0: 32.856
Accepted swap fraction in Temp 0: 0.013
Mean acceptance fraction Temp 0: 0.179
Mean log-likelihood: 591.319
Mean log-posterior: 591.319
Current log-posterior dispersion: 12.633
Current MAP: (0, 5) 600.654
Saving time: 0.03463 sec
Elapsed time: 27.5198 min
--------- Iteration: 6100
Mean tau Temp 0: 32.802
Accepted swap fraction in Temp 0: 0.013
Mean acceptance fraction Temp 0: 0.177
Mean log-likelihood: 590.659
Mean log-posterior: 590.659
Current log-posterior dispersion: 11.756
Current MAP: (0, 5) 601.747
Saving time: 0.01492 sec
Elapsed time: 27.9693 min
--------- Iteration: 6200
Mean tau Temp 0: 32.713
Accepted swap fraction in Temp 0: 0.013
Mean acceptance fraction Temp 0: 0.176
Mean log-likelihood: 590.907
Mean log-posterior: 590.907
Current log-posterior dispersion: 12.053
Current MAP: (0, 6) 601.996
Saving time: 0.02042 sec
Elapsed time: 28.4172 min
--------- Iteration: 6300
Mean tau Temp 0: 32.584
Accepted swap fraction in Temp 0: 0.014
Mean acceptance fraction Temp 0: 0.175
Mean log-likelihood: 591.352
Mean log-posterior: 591.352
Current log-posterior dispersion: 12.005
Current MAP: (0, 31) 601.244
Saving time: 0.02099 sec
Elapsed time: 28.8633 min
--------- Iteration: 6400
Mean tau Temp 0: 32.415
Accepted swap fraction in Temp 0: 0.014
Mean acceptance fraction Temp 0: 0.173
Mean log-likelihood: 591.46
Mean log-posterior: 591.46
Current log-posterior dispersion: 11.586
Current MAP: (0, 56) 599.849
Saving time: 0.02218 sec
Elapsed time: 29.3074 min
--------- Iteration: 6500
Mean tau Temp 0: 32.206
Accepted swap fraction in Temp 0: 0.015
Mean acceptance fraction Temp 0: 0.172
Mean log-likelihood: 590.341
Mean log-posterior: 590.341
Current log-posterior dispersion: 11.947
Current MAP: (0, 7) 600.17
Saving time: 0.02193 sec
Elapsed time: 29.7552 min
--------- Iteration: 6600
Mean tau Temp 0: 31.962
Accepted swap fraction in Temp 0: 0.015
Mean acceptance fraction Temp 0: 0.171
Mean log-likelihood: 590.171
Mean log-posterior: 590.171
Current log-posterior dispersion: 13.723
Current MAP: (0, 35) 600.731
Saving time: 0.02171 sec
Elapsed time: 30.1942 min
--------- Iteration: 6700
Mean tau Temp 0: 31.672
Accepted swap fraction in Temp 0: 0.016
Mean acceptance fraction Temp 0: 0.17
Mean log-likelihood: 591.619
Mean log-posterior: 591.619
Current log-posterior dispersion: 10.94
Current MAP: (0, 1) 600.322
Saving time: 0.02228 sec
Elapsed time: 30.6384 min
--------- Iteration: 6800
Mean tau Temp 0: 31.34
Accepted swap fraction in Temp 0: 0.017
Mean acceptance fraction Temp 0: 0.168
Mean log-likelihood: 591.258
Mean log-posterior: 591.258
Current log-posterior dispersion: 11.574
Current MAP: (0, 12) 601.623
Saving time: 0.02312 sec
Elapsed time: 31.0837 min
--------- Iteration: 6900
Mean tau Temp 0: 30.962
Accepted swap fraction in Temp 0: 0.017
Mean acceptance fraction Temp 0: 0.167
Mean log-likelihood: 591.518
Mean log-posterior: 591.518
Current log-posterior dispersion: 12.71
Current MAP: (0, 57) 601.191
Saving time: 0.02304 sec
Elapsed time: 31.5231 min
--------- Iteration: 7000
Mean tau Temp 0: 30.54
Accepted swap fraction in Temp 0: 0.018
Mean acceptance fraction Temp 0: 0.166
Mean log-likelihood: 591.962
Mean log-posterior: 591.962
Current log-posterior dispersion: 11.707
Current MAP: (0, 28) 601.51
Saving time: 0.02415 sec
Elapsed time: 31.9745 min
--------- Iteration: 7100
Mean tau Temp 0: 30.073
Accepted swap fraction in Temp 0: 0.019
Mean acceptance fraction Temp 0: 0.165
Mean log-likelihood: 592.833
Mean log-posterior: 592.833
Current log-posterior dispersion: 10.781
Current MAP: (0, 54) 601.075
Saving time: 0.02427 sec
Elapsed time: 32.4229 min
--------- Iteration: 7200
Mean tau Temp 0: 29.599
Accepted swap fraction in Temp 0: 0.019
Mean acceptance fraction Temp 0: 0.164
Mean log-likelihood: 591.413
Mean log-posterior: 591.413
Current log-posterior dispersion: 11.297
Current MAP: (0, 35) 602.045
Saving time: 0.02484 sec
Elapsed time: 32.8656 min
--------- Iteration: 7300
Mean tau Temp 0: 29.111
Accepted swap fraction in Temp 0: 0.02
Mean acceptance fraction Temp 0: 0.163
Mean log-likelihood: 591.781
Mean log-posterior: 591.781
Current log-posterior dispersion: 12.109
Current MAP: (0, 5) 602.121
Saving time: 0.02491 sec
Elapsed time: 33.3059 min
--------- Iteration: 7400
Mean tau Temp 0: 28.615
Accepted swap fraction in Temp 0: 0.02
Mean acceptance fraction Temp 0: 0.162
Mean log-likelihood: 591.568
Mean log-posterior: 591.568
Current log-posterior dispersion: 11.77
Current MAP: (0, 4) 601.852
Saving time: 0.02609 sec
Elapsed time: 33.7411 min
--------- Iteration: 7500
Mean tau Temp 0: 28.106
Accepted swap fraction in Temp 0: 0.021
Mean acceptance fraction Temp 0: 0.161
Mean log-likelihood: 592.026
Mean log-posterior: 592.026
Current log-posterior dispersion: 10.614
Current MAP: (0, 54) 602.372
Saving time: 0.02648 sec
Elapsed time: 34.18 min
--------- Iteration: 7600
Mean tau Temp 0: 27.59
Accepted swap fraction in Temp 0: 0.022
Mean acceptance fraction Temp 0: 0.16
Mean log-likelihood: 593.996
Mean log-posterior: 593.996
Current log-posterior dispersion: 9.115
Current MAP: (0, 10) 603.095
Saving time: 0.02643 sec
Elapsed time: 34.6233 min
--------- Iteration: 7700
Mean tau Temp 0: 27.066
Accepted swap fraction in Temp 0: 0.023
Mean acceptance fraction Temp 0: 0.159
Mean log-likelihood: 593.169
Mean log-posterior: 593.169
Current log-posterior dispersion: 9.74
Current MAP: (0, 45) 602.512
Saving time: 0.02750 sec
Elapsed time: 35.0649 min
--------- Iteration: 7800
Mean tau Temp 0: 26.535
Accepted swap fraction in Temp 0: 0.023
Mean acceptance fraction Temp 0: 0.158
Mean log-likelihood: 593.017
Mean log-posterior: 593.017
Current log-posterior dispersion: 10.49
Current MAP: (0, 50) 602.032
Saving time: 0.02751 sec
Elapsed time: 35.5018 min
--------- Iteration: 7900
Mean tau Temp 0: 25.979
Accepted swap fraction in Temp 0: 0.024
Mean acceptance fraction Temp 0: 0.157
Mean log-likelihood: 589.74
Mean log-posterior: 589.74
Current log-posterior dispersion: 15.577
Current MAP: (0, 6) 602.786
Saving time: 0.02764 sec
Elapsed time: 35.9426 min
--------- Iteration: 8000
Mean tau Temp 0: 25.436
Accepted swap fraction in Temp 0: 0.025
Mean acceptance fraction Temp 0: 0.156
Mean log-likelihood: 592.189
Mean log-posterior: 592.189
Current log-posterior dispersion: 12.297
Current MAP: (0, 0) 601.927
Saving time: 0.02883 sec
Elapsed time: 36.3792 min
--------- Iteration: 8100
Mean tau Temp 0: 24.877
Accepted swap fraction in Temp 0: 0.025
Mean acceptance fraction Temp 0: 0.155
Mean log-likelihood: 592.583
Mean log-posterior: 592.583
Current log-posterior dispersion: 10.815
Current MAP: (0, 29) 602.488
Saving time: 0.02836 sec
Elapsed time: 36.8166 min
--------- Iteration: 8200
Mean tau Temp 0: 24.313
Accepted swap fraction in Temp 0: 0.026
Mean acceptance fraction Temp 0: 0.154
Mean log-likelihood: 592.048
Mean log-posterior: 592.048
Current log-posterior dispersion: 12.367
Current MAP: (0, 3) 601.29
Saving time: 0.02922 sec
Elapsed time: 37.2473 min
--------- Iteration: 8300
Mean tau Temp 0: 23.739
Accepted swap fraction in Temp 0: 0.027
Mean acceptance fraction Temp 0: 0.153
Mean log-likelihood: 592.085
Mean log-posterior: 592.085
Current log-posterior dispersion: 11.59
Current MAP: (0, 34) 601.439
Saving time: 0.02921 sec
Elapsed time: 37.6747 min
--------- Iteration: 8400
Mean tau Temp 0: 23.164
Accepted swap fraction in Temp 0: 0.028
Mean acceptance fraction Temp 0: 0.152
Mean log-likelihood: 592.376
Mean log-posterior: 592.376
Current log-posterior dispersion: 10.486
Current MAP: (0, 32) 601.664
Saving time: 0.02840 sec
Elapsed time: 38.1054 min
--------- Iteration: 8500
Mean tau Temp 0: 22.581
Accepted swap fraction in Temp 0: 0.029
Mean acceptance fraction Temp 0: 0.151
Mean log-likelihood: 591.951
Mean log-posterior: 591.951
Current log-posterior dispersion: 11.883
Current MAP: (0, 26) 602.54
Saving time: 0.02946 sec
Elapsed time: 38.5357 min
--------- Iteration: 8600
Mean tau Temp 0: 21.988
Accepted swap fraction in Temp 0: 0.03
Mean acceptance fraction Temp 0: 0.15
Mean log-likelihood: 593.261
Mean log-posterior: 593.261
Current log-posterior dispersion: 10.121
Current MAP: (0, 51) 602.621
Saving time: 0.03271 sec
Elapsed time: 38.9637 min
--------- Iteration: 8700
Mean tau Temp 0: 21.392
Accepted swap fraction in Temp 0: 0.031
Mean acceptance fraction Temp 0: 0.149
Mean log-likelihood: 593.538
Mean log-posterior: 593.538
Current log-posterior dispersion: 10.461
Current MAP: (0, 32) 600.652
Saving time: 0.03186 sec
Elapsed time: 39.3985 min
--------- Iteration: 8800
Mean tau Temp 0: 20.783
Accepted swap fraction in Temp 0: 0.032
Mean acceptance fraction Temp 0: 0.148
Mean log-likelihood: 592.344
Mean log-posterior: 592.344
Current log-posterior dispersion: 11.158
Current MAP: (0, 55) 601.414
Saving time: 0.03170 sec
Elapsed time: 39.8294 min
--------- Iteration: 8900
Mean tau Temp 0: 20.177
Accepted swap fraction in Temp 0: 0.033
Mean acceptance fraction Temp 0: 0.148
Mean log-likelihood: 592.685
Mean log-posterior: 592.685
Current log-posterior dispersion: 9.778
Current MAP: (0, 32) 601.953
Saving time: 0.03329 sec
Elapsed time: 40.2593 min
--------- Iteration: 9000
Mean tau Temp 0: 19.561
Accepted swap fraction in Temp 0: 0.034
Mean acceptance fraction Temp 0: 0.147
Mean log-likelihood: 592.391
Mean log-posterior: 592.391
Current log-posterior dispersion: 10.778
Current MAP: (0, 24) 602.086
Saving time: 0.03355 sec
Elapsed time: 40.6949 min
--------- Iteration: 9100
Mean tau Temp 0: 18.944
Accepted swap fraction in Temp 0: 0.035
Mean acceptance fraction Temp 0: 0.146
Mean log-likelihood: 593.327
Mean log-posterior: 593.327
Current log-posterior dispersion: 10.025
Current MAP: (0, 6) 602.909
Saving time: 0.01602 sec
Elapsed time: 41.1285 min
--------- Iteration: 9200
Mean tau Temp 0: 18.309
Accepted swap fraction in Temp 0: 0.036
Mean acceptance fraction Temp 0: 0.145
Mean log-likelihood: 592.182
Mean log-posterior: 592.182
Current log-posterior dispersion: 11.7
Current MAP: (0, 56) 602.004
Saving time: 0.01996 sec
Elapsed time: 41.562 min
--------- Iteration: 9300
Mean tau Temp 0: 17.69
Accepted swap fraction in Temp 0: 0.037
Mean acceptance fraction Temp 0: 0.145
Mean log-likelihood: 592.618
Mean log-posterior: 592.618
Current log-posterior dispersion: 10.368
Current MAP: (0, 48) 600.896
Saving time: 0.02345 sec
Elapsed time: 41.9963 min
--------- Iteration: 9400
Mean tau Temp 0: 17.054
Accepted swap fraction in Temp 0: 0.038
Mean acceptance fraction Temp 0: 0.144
Mean log-likelihood: 592.589
Mean log-posterior: 592.589
Current log-posterior dispersion: 10.923
Current MAP: (0, 51) 602.344
Saving time: 0.02133 sec
Elapsed time: 42.4262 min
--------- Iteration: 9500
Mean tau Temp 0: 16.427
Accepted swap fraction in Temp 0: 0.039
Mean acceptance fraction Temp 0: 0.143
Mean log-likelihood: 593.121
Mean log-posterior: 593.121
Current log-posterior dispersion: 10.643
Current MAP: (0, 41) 603.223
Saving time: 0.02192 sec
Elapsed time: 42.8522 min
--------- Iteration: 9600
Mean tau Temp 0: 15.791
Accepted swap fraction in Temp 0: 0.041
Mean acceptance fraction Temp 0: 0.142
Mean log-likelihood: 594.587
Mean log-posterior: 594.587
Current log-posterior dispersion: 8.59
Current MAP: (0, 17) 602.992
Saving time: 0.02250 sec
Elapsed time: 43.2849 min
--------- Iteration: 9700
Mean tau Temp 0: 15.153
Accepted swap fraction in Temp 0: 0.042
Mean acceptance fraction Temp 0: 0.142
Mean log-likelihood: 593.477
Mean log-posterior: 593.477
Current log-posterior dispersion: 9.743
Current MAP: (0, 13) 602.626
Saving time: 0.02220 sec
Elapsed time: 43.7125 min
--------- Iteration: 9800
Mean tau Temp 0: 14.509
Accepted swap fraction in Temp 0: 0.043
Mean acceptance fraction Temp 0: 0.141
Mean log-likelihood: 592.113
Mean log-posterior: 592.113
Current log-posterior dispersion: 9.998
Current MAP: (0, 55) 601.271
Saving time: 0.02181 sec
Elapsed time: 44.1457 min
--------- Iteration: 9900
Mean tau Temp 0: 13.854
Accepted swap fraction in Temp 0: 0.044
Mean acceptance fraction Temp 0: 0.14
Mean log-likelihood: 592.492
Mean log-posterior: 592.492
Current log-posterior dispersion: 9.567
Current MAP: (0, 40) 602.343
Saving time: 0.02403 sec
Elapsed time: 44.5739 min
--------- Iteration: 10000
Mean tau Temp 0: 13.199
Accepted swap fraction in Temp 0: 0.045
Mean acceptance fraction Temp 0: 0.14
Mean log-likelihood: 592.495
Mean log-posterior: 592.495
Current log-posterior dispersion: 10.627
Current MAP: (0, 6) 603.27
Saving time: 0.02273 sec
Elapsed time: 45.0122 min
--------- Iteration: 10100
Mean tau Temp 0: 12.533
Accepted swap fraction in Temp 0: 0.046
Mean acceptance fraction Temp 0: 0.139
Mean log-likelihood: 591.468
Mean log-posterior: 591.468
Current log-posterior dispersion: 11.326
Current MAP: (0, 2) 602.391
Saving time: 0.02415 sec
Elapsed time: 45.445 min
--------- Iteration: 10200
Mean tau Temp 0: 11.889
Accepted swap fraction in Temp 0: 0.048
Mean acceptance fraction Temp 0: 0.138
Mean log-likelihood: 592.773
Mean log-posterior: 592.773
Current log-posterior dispersion: 9.205
Current MAP: (0, 15) 602.257
Saving time: 0.02389 sec
Elapsed time: 45.8773 min
--------- Iteration: 10300
Mean tau Temp 0: 11.237
Accepted swap fraction in Temp 0: 0.049
Mean acceptance fraction Temp 0: 0.137
Mean log-likelihood: 592.169
Mean log-posterior: 592.169
Current log-posterior dispersion: 9.896
Current MAP: (0, 59) 602.54
Saving time: 0.02401 sec
Elapsed time: 46.3144 min
--------- Iteration: 10400
Mean tau Temp 0: 10.59
Accepted swap fraction in Temp 0: 0.05
Mean acceptance fraction Temp 0: 0.137
Mean log-likelihood: 593.359
Mean log-posterior: 593.359
Current log-posterior dispersion: 9.266
Current MAP: (0, 53) 603.288
Saving time: 0.02558 sec
Elapsed time: 46.7459 min
--------- Iteration: 10500
Mean tau Temp 0: 9.946
Accepted swap fraction in Temp 0: 0.051
Mean acceptance fraction Temp 0: 0.136
Mean log-likelihood: 592.585
Mean log-posterior: 592.585
Current log-posterior dispersion: 10.788
Current MAP: (0, 14) 601.746
Saving time: 0.02638 sec
Elapsed time: 47.1813 min
--------- Iteration: 10600
Mean tau Temp 0: 9.303
Accepted swap fraction in Temp 0: 0.052
Mean acceptance fraction Temp 0: 0.135
Mean log-likelihood: 593.065
Mean log-posterior: 593.065
Current log-posterior dispersion: 9.159
Current MAP: (0, 6) 601.404
Saving time: 0.02734 sec
Elapsed time: 47.6251 min
--------- Iteration: 10700
Mean tau Temp 0: 8.673
Accepted swap fraction in Temp 0: 0.054
Mean acceptance fraction Temp 0: 0.135
Mean log-likelihood: 592.702
Mean log-posterior: 592.702
Current log-posterior dispersion: 9.269
Current MAP: (0, 30) 601.796
Saving time: 0.02680 sec
Elapsed time: 48.0684 min
--------- Iteration: 10800
Mean tau Temp 0: 8.052
Accepted swap fraction in Temp 0: 0.055
Mean acceptance fraction Temp 0: 0.134
Mean log-likelihood: 594.523
Mean log-posterior: 594.523
Current log-posterior dispersion: 7.337
Current MAP: (0, 21) 601.586
Saving time: 0.02729 sec
Elapsed time: 48.5059 min
--------- Iteration: 10900
Mean tau Temp 0: 7.438
Accepted swap fraction in Temp 0: 0.056
Mean acceptance fraction Temp 0: 0.134
Mean log-likelihood: 593.254
Mean log-posterior: 593.254
Current log-posterior dispersion: 8.242
Current MAP: (0, 55) 602.951
Saving time: 0.02778 sec
Elapsed time: 48.94 min
--------- Iteration: 11000
Mean tau Temp 0: 6.839
Accepted swap fraction in Temp 0: 0.057
Mean acceptance fraction Temp 0: 0.133
Mean log-likelihood: 593.073
Mean log-posterior: 593.073
Current log-posterior dispersion: 9.26
Current MAP: (0, 20) 602.555
Saving time: 0.02992 sec
Elapsed time: 49.382 min
--------- Iteration: 11100
Mean tau Temp 0: 6.263
Accepted swap fraction in Temp 0: 0.058
Mean acceptance fraction Temp 0: 0.132
Mean log-likelihood: 592.902
Mean log-posterior: 592.902
Current log-posterior dispersion: 9.344
Current MAP: (0, 31) 603.059
Saving time: 0.02934 sec
Elapsed time: 49.8217 min
--------- Iteration: 11200
Mean tau Temp 0: 5.717
Accepted swap fraction in Temp 0: 0.059
Mean acceptance fraction Temp 0: 0.132
Mean log-likelihood: 593.967
Mean log-posterior: 593.967
Current log-posterior dispersion: 8.226
Current MAP: (0, 6) 602.107
Saving time: 0.02902 sec
Elapsed time: 50.2597 min
--------- Iteration: 11300
Mean tau Temp 0: 5.212
Accepted swap fraction in Temp 0: 0.06
Mean acceptance fraction Temp 0: 0.131
Mean log-likelihood: 594.13
Mean log-posterior: 594.13
Current log-posterior dispersion: 7.664
Current MAP: (0, 52) 601.676
Saving time: 0.03001 sec
Elapsed time: 50.7011 min
--------- Iteration: 11400
Mean tau Temp 0: 4.753
Accepted swap fraction in Temp 0: 0.061
Mean acceptance fraction Temp 0: 0.131
Mean log-likelihood: 592.933
Mean log-posterior: 592.933
Current log-posterior dispersion: 9.153
Current MAP: (0, 34) 601.799
Saving time: 0.03144 sec
Elapsed time: 51.1419 min
--------- Iteration: 11500
Mean tau Temp 0: 4.376
Accepted swap fraction in Temp 0: 0.062
Mean acceptance fraction Temp 0: 0.13
Mean log-likelihood: 593.308
Mean log-posterior: 593.308
Current log-posterior dispersion: 7.777
Current MAP: (0, 32) 601.047
Saving time: 0.03209 sec
Elapsed time: 51.5897 min
--------- Iteration: 11600
Mean tau Temp 0: 4.123
Accepted swap fraction in Temp 0: 0.063
Mean acceptance fraction Temp 0: 0.13
Mean log-likelihood: 592.397
Mean log-posterior: 592.397
Current log-posterior dispersion: 9.015
Current MAP: (0, 13) 603.379
Saving time: 0.03281 sec
Elapsed time: 52.0291 min
--------- Iteration: 11700
Mean tau Temp 0: 4.081
Accepted swap fraction in Temp 0: 0.065
Mean acceptance fraction Temp 0: 0.129
Mean log-likelihood: 592.404
Mean log-posterior: 592.404
Current log-posterior dispersion: 9.75
Current MAP: (0, 0) 603.246
Saving time: 0.03326 sec
Elapsed time: 52.4725 min
--------- Iteration: 11800
Mean tau Temp 0: 4.415
Accepted swap fraction in Temp 0: 0.066
Mean acceptance fraction Temp 0: 0.128
Mean log-likelihood: 593.166
Mean log-posterior: 593.166
Current log-posterior dispersion: 8.746
Current MAP: (0, 25) 601.985
Saving time: 0.03375 sec
Elapsed time: 52.9099 min
--------- Iteration: 11900
Mean tau Temp 0: 5.639
Accepted swap fraction in Temp 0: 0.067
Mean acceptance fraction Temp 0: 0.128
Mean log-likelihood: 594.105
Mean log-posterior: 594.105
Current log-posterior dispersion: 7.68
Current MAP: (0, 17) 603.018
Saving time: 0.03422 sec
Elapsed time: 53.3422 min
--------- Iteration: 12000
Mean tau Temp 0: 12.046
Accepted swap fraction in Temp 0: 0.068
Mean acceptance fraction Temp 0: 0.127
Mean log-likelihood: 593.287
Mean log-posterior: 593.287
Current log-posterior dispersion: 8.095
Current MAP: (0, 29) 603.026
Saving time: 0.03460 sec
Elapsed time: 53.7798 min
--> Maximum number of iterations reached in MCMC
--> Best solutions from the ./MySystem.hdf5 will be written at: ./MySystem.best
--> Reference epoch of the solutions: 0 [JD]
--> Iterations performed: 12000
--> Elapsed time in MCMC: 53.7799 minutes
Out[11]:
<ptemcee.sampler.Sampler at 0x7f101ddb0390>
Print a summary of the results and get a dictionary with the posteriors. Let's make first a burnin of the first 20% of the chains. This burnin will be applied over the posteriors.
In [12]:
burn = 0.2
In [13]:
posteriors = nau.utils.mcmc_summary(PS,
hdf5_file=mcmc.hdf5_filename,
burnin=burn,
get_posteriors=True)
--> Planetary System: MySystem
Stellar mass: 0.522
Stellar radius: 0.4422
Number of planets: 3
--> Planets:
Planet 1: Planet-b
Planet 2: Planet-c
Planet 3: Planet-d
--------------------------
--> MCMC parameters
Ntemps: 12
Nwalkers per temperature: 60
Number of iterations: 12000
Thining: 100
Burnin: 0.2
Chain shape: (60, 97, 18)
--------------------------
RESULTS
--> Results in File: ./MySystem.hdf5
--> Reference epoch of the solutions: 0 [JD]
--> Best solution in MCMC
Logl: 603.37856
mass period ecc inclination argument mean_anomaly ascending_node
Planet 1: 0.0738 10.4708 0.0431 90.0 256.1075 285.7213 100.8759
Planet 2: 2.1322 14.105 0.0419 91.1692 216.4375 217.1319 102.3262
Planet 3: 0.7461 23.5749 0.0191 90.3 355.4471 234.6966 88.5
--------------------------
--> MCMC medians and 1-sigma errors
mass1 0.06 ^{+0.028}_{-0.022}
period1 10.47084 ^{+0.000159}_{-0.000101}
ecc1 0.042 ^{+0.00358}_{-0.00394}
argument1 246.2 ^{+7.046}_{-9.86}
mean_anomaly1 296.43 ^{+10.679}_{-7.727}
ascending_node1 103.89 ^{+3.301}_{-4.629}
mass2 2.04 ^{+0.344}_{-0.374}
period2 14.11 ^{+0.0}_{-0.0}
ecc2 0.05 ^{+0.008}_{-0.005}
inclination2 90.62 ^{+0.479}_{-0.941}
argument2 207.79 ^{+4.314}_{-5.921}
mean_anomaly2 226.64 ^{+6.707}_{-4.858}
ascending_node2 106.4 ^{+3.448}_{-3.637}
mass3 0.72 ^{+0.18}_{-0.17}
period3 23.57 ^{+0.0}_{-0.001}
ecc3 0.04 ^{+0.011}_{-0.015}
argument3 355.49 ^{+2.629}_{-4.424}
mean_anomaly3 231.54 ^{+4.282}_{-3.316}
Plot a pair of results. Let's show the masses space for these three planets, where the colors are related to the iterations progress
In [14]:
# See the available keys in posteriors
print("\nAvailable posteriors are:")
print(list(posteriors.keys()))
print()
post1 = 'mass1'
post2 = 'mass2'
post3 = 'mass3'
# Colors show the movement forward
lburn = mcmc.itmax*burn
nsave = int(len(posteriors[post1])/mcmc.nwalkers)
steps = np.array([[lburn+(i*mcmc.intra_steps)]*mcmc.nwalkers for i in range(nsave)]).flatten()
fig, axes = plt.subplots(1,2, figsize=(12,6))
axes[0].scatter(posteriors[post1], posteriors[post2],c=steps,
edgecolor='w',cmap='GnBu')
axes[0].set_xlabel(post1)
axes[0].set_ylabel(post2)
im=axes[1].scatter(posteriors[post2], posteriors[post3],c=steps,
edgecolor='w',cmap='GnBu')
axes[1].set_xlabel(post2)
axes[1].set_ylabel(post3)
plt.colorbar(im).set_label('Iteration')
plt.savefig(f'3pl_{post1}_{post2}_{post3}.jpg')
Available posteriors are: ['mass1', 'period1', 'ecc1', 'argument1', 'mean_anomaly1', 'ascending_node1', 'mass2', 'period2', 'ecc2', 'inclination2', 'argument2', 'mean_anomaly2', 'ascending_node2', 'mass3', 'period3', 'ecc3', 'argument3', 'mean_anomaly3']
Plot a pair of built-in figures from the nauyaca's Plots module. -burnin- will discard the first 20% of the initial chains
In [15]:
nauplot = nau.Plots(PS, hdf5_file=mcmc.hdf5_filename, burnin=burn, temperature=0)
In [16]:
# Plot the fitted TTVs
nauplot.TTVs(nsols=10,
mode='random' # 'best'
);
plt.savefig('3pl_TTVs.jpg')
--> plotting random solutions
In [17]:
# Plot a croner plot
nauplot.corner_plot();
plt.savefig('3pl_corner.jpg')
In [18]:
# Plot histograms of the posteriors
nauplot.hist(titles=True);
plt.savefig('3pl_hist.jpg')
Compare your results! The true planetary parameters for this synthetic system are stored in './inputs/trues':
Planet mass period ecc inc argument mean_anomaly asc_node
1 0.07652, 10.4707, 0.0406, 89.809, 292.62, 246.14, 88.3,
2 1.98033, 14.10509, 0.0244, 89.909, 239.76, 191.31, 88.46,
3 0.6705, 23.57467, 0.0306, 90.336, 82.64, 149.24, 88.51In example 'restarting_mcmc' we'll see how to restart the mcmc to make more iterations and improve the results.
Quitar todo lo que sigue¶
In [53]:
nauplot.temperature=10
In [19]:
nauplot.trace_plot(plot_means=True);
In [20]:
nauplot.convergence();
--> Performing Gelman-Rubin test --> Performing Geweke test
In [21]:
nauplot.monitor();
